Contradiction with Proverbs 28:9
Proverbs 28:9 suggests that the prayers of a person who turns away from hearing the law are an abomination, which contrasts with the positive assurance of answered prayer in Psalms 20:1.
Proverbs 28:9: He that turneth away his ear from hearing the law, even his prayer [shall be] abomination.
Contradiction with James 4:3
James 4:3 states that prayers can go unanswered if they are asked with the wrong motives, contrasting Psalms 20:1's assurance of the Lord hearing in times of trouble.
James 4:3: Ye ask, and receive not, because ye ask amiss, that ye may consume [it] upon your lusts. [lusts: or, pleasures]
Contradiction with Isaiah 1:15
Isaiah 1:15 explains that God may not listen to prayers when hands are full of blood, contradicting the assurance in Psalms 20:1 that God will hear in times of trouble.
Isaiah 1:15: And when ye spread forth your hands, I will hide mine eyes from you: yea, when ye make many prayers, I will not hear: your hands are full of blood. [make...: Heb. multiply prayer] [blood: Heb. bloods]
Contradiction with Job 35:13
Job 35:13 mentions that God does not hear vanity, contrasting with Psalms 20:1's affirmation of God answering calls for help.
Job 35:13: Surely God will not hear vanity, neither will the Almighty regard it.